I don't think this is an issue that should ever be put to a popular vote really, but ignoring that fact, if the people of the UK want to have a public vote on rejoining the EU in the future, I don't have a problem with that.Does honoring a vote and accepting its repercussions mean never holding a second vote on the issue in the future?
Just because a decision is made once doesn't mean it should be set in stone forever, with no chance of ever being overturned or rolled back. I don't see a second referendum happening, I think Cameron's resignation gave the Leave win all the legitimacy it needs (aside from, well, the win itself!), but I also think the idea of "It doesn't matter whether peple regret it, we just need to accept it and move it on" is fairly antithetical to the whole idea of voting. You don't just vote once on something and let it stay that way forever (well, you could, but you don't have to).